Question

Arc length of polar curves. Find arc lenngth of complete circle r = asin(theta) ; a>0.

Answer 1

Pretty clear on how to find arc length but I think I have the wrong bounds of integration. I got 2pi*a as answer and my book shows pi*a and noted that the bounds of integration where just 0 to pi since that asin(theta) is diameter of circle and that full circle is transversed over interval o to pi.......can someone please help explain this.

Answer 2

\[\int\limits_{lower}^{upper} \sqrt{r^2+(\frac{dr}{d \theta})^2} d \theta \\ r=a \sin(\theta)\]
so we used the integral right?

Answer 3

you should have got pia with those bounds

Answer 4

if you used that integral setup

Answer 5

you said you used 0=lower and pi=upper?

Answer 6

I bet you messed on the trig identity part maybe..
Not totally sure but let's say you did...
\[\sqrt{a^2 \sin^2(\theta)+a^2 \cos^2(\theta)}=\sqrt{a^2(\sin^2(\theta)+\cos^2(\theta))} =\sqrt{a^2(1)} \\ =\sqrt{a^2}=a \text{ since } a>0\]

Answer 7

No I used 0 lower pi upper limits, and the book said to use 0 lower pi upper. I thought since we are in polar to integrate a full circle you would go from 0 to 2pi.

Answer 8

oh...no it should be x=0 to pi
r=asin(u)
u | r
0 a(0)=0
pi/2 | a(1)=a
pi | a(0)=0
0 to pi gives that complete rotation

Answer 9

because it comes back around to 0

Answer 10

do you know how graph polor coordinates?

Answer 11

polar*

Answer 12

if we do theta=0 to theta=2pi
it will take us around again

Answer 13

u | r
3pi/2, -a